What Happens to Energy Levels in a Reduced Potential Well?

[indie452]

if V is reduced to much smaller than the zero point energy then what happens to the ground state and first excited state?


for this i know that the function becomes continuous and that the particle is unbound. does this mean that the function will also just have an oscillatory form?

 

[morphemera]

What are you asking exactly? you should know that shifting of potential V with a constant value Vo does not change the wavefunction.

 

[indie452]

yeah but if you change V from it being originally greater than E to being much smaller than the zero point energy surely this would change the ground and first excited wave function? wouldn't the fact that the E of the function is greater than V mean that it is no longer bound by the potential well?

i have these ideas but I am not sure if they are right and unfortunately this is not looked at in any of the books I've read.

 

[indie452]

so after thinking on it believe the ground state would stay the same as is the zero point energy which doesn't change, but then would the 1st excited state have enough energy to become unbound from the potential well